Evaluate `(2^(n)+ 2^(n-1))/(2^(n+1) - 2^(n))`

Find the value of ((2^(n)+2^(n-1))/(2^(n+1)-2^(n)))

Evaluate : (a^(2n+1) xx a^((2n+1)(2n-1)))/(a^(n(4n-1)) xx (a^2)^(2n+3)

Divide x^(2n)+a^(2^(n-1))x^(2^(n-1))+a^(2^(n))byx^(2^(n-1))-a^(2^(n-2))x^(2^(n-2))+a^(2^(n-1))

Find sum of sum_(r=1)^n r . C (2n,r) (a) n*2^(2n-1) (b) 2^(2n-1) (c) 2^(n-1)+1 (d) None of these

Evaluate : sum_(n=1)^(15) (2n+1)2^n .

Evaluate sum_(n=1)^n (n^2+n-1)/((n+2)!) .

Evaluate lim_(n rarr oo)n[(1)/((n+1)(n+2))+(1)/((n+2)(n+4))++(1)/(6n^(2))]

If A=([x,x],[x,x]) then A^(n)(n in N)= 1) ([2^nx^n,2^nx^n],[2^nx^n,2^nx^n]) 2) ([2^(n-1) x^n,2^(n-1) x^n],[2^(n-1) x^n,2^(n-1) x^n]) 3) I 4) ([2^(n) x^(n-1),2^(n) x^(n-1)],[2^(n) x^(n-1),2^(n) x^(n-1)])

Evaluate: lim_(n rarr oo)[(1)/((n+1)^(2))+(1)/((n+2)^(2))+...+(1)/((2n)^(2))]

Evaluate lim_(ntooo) n^(-n^(2))[(n+2^(0))(n+2^(-1))(n+2^(-2))...(n+2^(-n+1))]^(n) .